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LINTON UNIVERSITY COLLEGE SCHOOL OF CIVIL ENGINEERING GEO-MECHANICS (CE2204) Shear Strength of Soils Lecture Week No 4 Mdm Nur Syazwani Noor Rodi NOTATIONS σ - Total Stress [kN/m2; kPa] σ’ - Effective Stress [kN/m2; kPa] σN - Normal Stress [kN/m2; kPa] σv - Vertical Total Stress [kN/m2; kPa] σh - Horizontal Total Stress [kN/m2; kPa] σ1 - Principle Stress [kN/m2; kPa] σ3 - Minor Stress [kN/m2; kPa] u - Pore Water Pressure [kN/m2; kPa] - Shear Strength [kN/m2; kPa] Φ - Angle of Friction [º] Δ - Change in C - Cohesion of Soils [kN/m2; kPa] SHEAR FAILURE IN SOILS WHAT IS SHEAR STRENGTH? • The shear strength of a soil is its resistance to shearing stresses. • It is a measure of the soil resistance to deformation by continuous displacement of its individual soil particles • Shear strength in soils depends primarily on interactions between particles • Shear failure occurs when the stresses between the particles are such that they slide over each other SHEAR STRENGTH IN SOILS q STRIP FOOTING Shear Stress, Shear Resistance, f The soil grains slide over each other along the failure surface At failure, shear stress along the failure surface () reaches the shear strength (f). SHEAR STRENGTH PARAMETERS Soil derives its shear strength from two sources: a) Cohesion (C), is a measurement of the forces that cement between particles of soils (stress independent component) - Cementation between sand grains - Electrostatic attraction between clay particles b) Internal Friction angle (Φ), is the measure of the frictional resistance between particles of soils (stress dependent component) MOHR-COULOMB FAILURE CRITERION This theory states that a material failure is due to the critical combination of normal stress and shear stress The relationship between normal stress and shear is given as…… MOHR-COULOMB FAILURE CRITERION f c N tan MOHR CIRCLE σ1 = σ3 + Δσv c tan N σ3 f σ3 SOIL ELEMENT General State of Stress v σ3 σ1 MOHR CIRCLE σ1 = σ3 + Δσv As loading progresses, Mohr circle becomes larger… N σ3 f σ3 SOIL ELEMENT General State of Stress Initially, Mohr circle is a point .. and finally failure occurs when Mohr circle touches the envelope TYPES OF SHEAR TEST Laboratory Tests: a) Shear Box b) Triaxial Compression In Situ Tests: a) Standard Penetration b) Shear Vane UNDRAINED TESTS • NO drainage of pore water • simulates short term condition (e.g. end of construction) • excess pore water pressure, Δu is often finite DRAINED TEST • Drainage ALLOW for pore water • simulates long term condition (e.g. ‘many years’ after construction) • excess pore water pressure, Δu = 0; however u is not necessarily = 0 TYPES OF SHEAR TEST (DIRECT SHEAR BOX) TYPES OF SHEAR TEST (DIRECT SHEAR BOX) max (kN/m2) TYPES OF SHEAR TEST (DIRECT SHEAR BOX) f Cd N tand Φd ● ● ● (N3 , 3) (N2 , 2) (N1 , 1) Cd N (kN/m2) Example 1 A drained shear box test was carried out on a sandy clay and yielded for the following results: Normal Load (N) 108 202 295 390 484 576 Shear Load at failure (N) 172 227 266 323 374 425 Area of shear plane = 60mm x 60mm Determine the apparent cohesion and angle of friction for the soil Example 2 Test Maximum Shear Stress (kN/m2) Normal Load, P (kg) Normal Stress, N (kN/m2) max 1 70 P A 36.7 36.7 9.81 2 1000 0.06 100 9.81 2 1000 0.06 200 9.81 2 1000 0.06 350 2 130 73.4 73.4 3 220 128.4 128.4 TYPES OF SHEAR TEST (TRIAXIAL TEST) TYPES OF SHEAR TEST (TRIAXIAL TEST) • The test is designed to mimic actual field or “in situ” conditions of the soil. • Triaxial tests are run by: 1. saturating the soil 2. applying the confining stress (σ3) 3. applying the vertical stress (known as deviator stress) until failure • 3 main types of triaxial tests: a) Unconsolidated - Undrained b) Consolidated – Drained c) Consolidated – Undrained UNDRAINED TEST (Unconsolidated-Undrained) σ3 0 0 u≈0 0 σ3 u≠0 σ1 σ3 σ3 uf ≠ 0 Undrained Undrained Stage A Stage B Stage C Sample Preparation Apply Cell Pressure Undrained Failure • Fast - Undrained - Short term • Cu & Φu • for saturated soils (S=1), NO Volume Change σ3 DRAINED TEST (Consolidated-Drained) σ3 0 0 u≈0 0 σ3 u=0 σ1 σ3 σ3 uf = 0 Drained Drained Stage A Stage B Stage C Sample Preparation Consolidation Drained Failure • Extremely slow – Drained – Long term • Cd & Φd • for saturated soils (S=1), NO Volume Change σ3 CONSOLIDATED UNDRAINED TEST σ3 0 0 u≈0 0 σ3 u=0 σ1 σ3 σ3 uf ≠ 0 Drained Undrained Stage A Stage B Stage C Sample Preparation Consolidation Undrained Failure • Intermediate – Drained – Long & Short term • C’ & Φ’ ( ≈ Cd & Φd ) ; Cu & Φu σ3 Example 1 A drained triaxial compression test carried out on three specimens of the same soil yielded the following results: Test No. 1 2 3 Cell pressure (kPa) 100 200 300 Deviator stress at failure (kPa) 210 438 644 Draw the shear strength envelop and determine the shear strength parameters, C’ & Φ’, assuming that the pore water pressure remain constant during the axial loading stage. Example 2 Three consolidation undrained triaxial tests were carried out on 38mm diameter samples of the same clay. The applied axial force at failure of the samples were found to be as follows:Test No. 1 2 3 Cell pressure (kN/m2) 25 75 120 0.086 0.120 0.149 Applied axial force at failure (kN) Determine the shear strength parameters of the clay in term of total stress. Example 3 The following results were obtained from undrained triaxial tests on specimens of a saturated normally consolidated clay. Test No. 1 2 3 Cell Pressure (kN/m2) 100 200 300 Ultimate Deviator Stress (kN/m2) 137 210 283 Ultimate Pore Pressure (kN/m2) 28 86 147 Determine the shear strength parameters of the clay in term of total and effective stress. Example 4 The following results were obtained from undrained triaxial tests on specimens of an overconsolidated clay. Test No. 1 2 3 Cell Pressure (kN/m2) 100 250 400 Deviator Stress at failure (kN/m2) 340 410 474 Deviator Pore Pressure (kN/m2) -42 64 177 Determine the shear strength parameters of the clay in term of total and effective stress. Example 5 Referring to Example 2, if the shear strength parameters of the clay in term of effective stress were C’ = 10 kN/m2 and Φ’ = 30°, determine the pore water pressure in each sample at failure. Example 6 Consolidated undrained triaxial tested were carried out on 3 samples of the same clay soil and the following results were obtained at the point of failure:Sample No. Cell Pressure (kN/m2) Deviator Stress at failure (kN/m2) Pore Water Pressure (kN/m2) 1 50 80.543 27.201 2 100 ? 57.879 3 ? 158.514 ? Cu Φu C’ Φ’ (kN/m2) (°) (kN/m2) (°) 10 ? ? ? Determine the 6 unknown value (?) in the table by Calculation and Graphical method TYPES OF SHEAR TEST (SHEAR VANE TEST) d 2h d 3 T Cu 6 2 TYPES OF SHEAR TEST (SHEAR VANE TEST) • Suitable for determining the in-situ undrained shear strength of unfissured saturated clays and silts • The vane consists of four rectangular blades in a cruciform at the end of a steel rod • Shear strength is measure by pushing the vane into the soil and rotated by applying a torque at the surface end of the rod • The vane is first rotated at 6-12° per minute to determine the undisturbed shear strength and then the remoulded strength is measured by rotating the vane rapidly Example 1 A shear vane used to test a soft clay had a diameter of 75mm and a length of 150mm. The average torques recorded after slow and then rapid rotations were 64 and 26 Nm respectively. Determine the undrained strength of the clay.